Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C5×D4 ⋊ C22 |
| Hall | C3×C5 ⋊ H(5,𝔽2) |
| Sylow | C5 ⋊ #1004 |
| Sylow | C3 ⋊ #4144 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×D5 |
| commutator, socle, cosocle | C2×C3×C5 | C24 |
| Fitting | C3×C5×D4 | C22 |
| hypercenter | D4 | D3×D5 |
| hypocenter | C3×C5 | H(5,𝔽2) |
| LCS | G ▷ C2×C3×C5 ▷ C3×C5 | |
| UCS | C1 ◁ C2 ◁ D4 | |
332 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 4 generators on 16 points:
(1,2,4,5,3)(6,7,8)(10,14)(11,15);(9,11)(10,13)(12,15)(14,16);(7,8)(11,15)(13,16);(2,3)(4,5)(9,10)(11,13)(12,14)(15,16)Polycyclic presentation:
2^5,3,5|d^a=de,g^a=g^4,c^b=ce,f^b=f^2,d^c=de57 conjugacy classes — view the full character table.
| maximal subgroup of | #11754054, #11754055, #11754056, … |
| maximal normal subgroup of | #11754054, #11754055, #11754056, … |
| maximal quotient of | #11752795, #11752807, #11752810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1101);